A General Framework for Constructing Local Hidden-state Models to Determine the Steerability

TL;DR

This paper introduces a machine learning framework to construct local hidden-state models, enabling the determination of quantum steerability for entangled states, validated on Werner and isotropic states with results matching known bounds.

Contribution

The authors develop a novel machine learning approach to efficiently construct LHS models, advancing the detection of quantum steerability beyond traditional analytical methods.

Findings

Saturates analytical bounds for Werner states under various measurements

Achieves known bounds for isotropic states under PVMs

POVMs can reveal steerability where PVMs cannot

Abstract

Not all entangled states can exhibit quantum steering, and determining whether a given entangled state is steerable is a crucial problem in quantum information theory. The main challenge lies in verifying the existence of a local hidden-state (LHS) model capable of reproducing all post-measurement assemblages generated by arbitrary measurements. To address this, we propose a machine learning-based framework that employs batch sampling of measurements and gradient-based optimization to construct an optimal LHS model. We validate our method by analyzing the steerability of two-qubit Werner and two-qutrit isotropic states. For Werner states, our approach saturates the analytical visibility bounds under three Pauli measurements, arbitrary projective measurements (PVMs), and arbitrary positive operator-valued measurements (POVMs). For isotropic states, we achieve the known analytical bounds under arbitrary PVMs. We further investigate the steerability of this class of states under arbitrary POVMs, and our results suggest that POVMs can offer an advantage over PVMs in revealing the steerability of such states.